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An answer to a question of Kegel on sums of rings

Published:1998-03-01
Printed: Mar 1998
• A. V. Kelarev
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Abstract

We construct a ring $R$ which is a sum of two subrings $A$ and $B$ such that the Levitzki radical of $R$ does not contain any of the hyperannihilators of $A$ and $B$. This answers an open question asked by Kegel in 1964.
 MSC Classifications: 16N40 - Nil and nilpotent radicals, sets, ideals, rings 16N60 - Prime and semiprime rings [See also 16D60, 16U10]